Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 970 · 40 sums

The method (Split into easy parts): (a + b)² = a² + 2ab + b². (a − b)² = a² − 2ab + b². (a + b)(a − b) = a² − b²; so a² − b² = (a + b)(a − b). a² + b² = (a + b)² − 2ab = (a − b)² + 2ab.

1. 1.If a − b = 5 and ab = 36, what is a² + b²?
2. 2.Use (a + b)² = a² + 2ab + b² to find 98².
3. 3.Use a² − b² = (a + b)(a − b) to find 49² − 35².
4. 4.Use (a − b)² = a² − 2ab + b² to find 55².
5. 5.Use (a + b)² = a² + 2ab + b² to find 107².
6. 6.Use (a − b)² = a² − 2ab + b² to find 21².
7. 7.Use (a − b)² = a² − 2ab + b² to find 56².
8. 8.Use (a − b)² = a² − 2ab + b² to find 91².
9. 9.Use (a − b)² = a² − 2ab + b² to find 38².
10. 10.Use (a + b)(a − b) = a² − b² to find 76 × 64.
11. 11.Use (a + b)² = a² + 2ab + b² to find 89².
12. 12.Find the value of x² − y² when x = 6 and y = 1.
13. 13.Use a² − b² = (a + b)(a − b) to find 93² − 73².
14. 14.Use (a + b)(a − b) = a² − b² to find 73 × 67.
15. 15.If a + b = 3 and ab = 2, what is a² + b²?
16. 16.If a + b = 8 and ab = 12, what is a² + b²?
17. 17.Use (a + b)² = a² + 2ab + b² to find 42².
18. 18.Use a² − b² = (a + b)(a − b) to find 68² − 40².
19. 19.Use a² − b² = (a + b)(a − b) to find 20² − 16².
20. 20.Use a² − b² = (a + b)(a − b) to find 32² − 24².
21. 21.Use (a + b)(a − b) = a² − b² to find 53 × 47.
22. 22.If a − b = 2 and ab = 15, what is a² + b²?
23. 23.Use (a − b)² = a² − 2ab + b² to find 16².
24. 24.Find the value of x² − y² when x = 5 and y = 4.
25. 25.Use (a + b)(a − b) = a² − b² to find 35 × 25.
26. 26.Use a² − b² = (a + b)(a − b) to find 62² − 14².
27. 27.Use (a + b)² = a² + 2ab + b² to find 58².
28. 28.Use (a + b)(a − b) = a² − b² to find 23 × 17.
29. 29.Use a² − b² = (a + b)(a − b) to find 88² − 8².
30. 30.Find the value of x² + 2xy + y² when x = 8 and y = 4.
31. 31.Use (a + b)² = a² + 2ab + b² to find 59².
32. 32.If a + b = 10 and ab = 16, what is a² + b²?
33. 33.If a + b = 9 and ab = 14, what is a² + b²?
34. 34.Use (a − b)² = a² − 2ab + b² to find 33².
35. 35.Use (a + b)(a − b) = a² − b² to find 66 × 54.
36. 36.Use (a + b)(a − b) = a² − b² to find 24 × 16.
37. 37.Use a² − b² = (a + b)(a − b) to find 62² − 6².
38. 38.Use (a − b)² = a² − 2ab + b² to find 39².
39. 39.Use (a + b)² = a² + 2ab + b² to find 61².
40. 40.Use (a − b)² = a² − 2ab + b² to find 75².

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